Starspot evolution, differential rotation, and magnetic cycles in the chromospherically active binaries lambda andromedae, sigma Geminorum, II Pegasi, and V711 Tauri

We have analyzed 15-19 yr of photoelectric photometry, obtained manually and with automated telescopes, of the chromospherically active binaries lambda And, sigma Gem, II Peg, and V711 Tau. These observations let us identify individual dark starspots on the stellar surfaces from periodic dimming of the starlight, follow the evolution of these spots, and search for long-term cyclic changes in the properties of these starspots that might reveal magnetic cycles analogous to the Sun's 11 yr sunspot cycle. We developed a computer code to fit a simple two-spot model to our observed light curves that allows us to extract the most easily determinable and most reliable spot parameters from the light curves, i.e., spot longitudes and radii. We then used these measured properties to identify individual spots and to chart their life histories by constructing migration and amplitude curves. We identified and followed 11 spots in lambda And, 16 in sigma Gem, 12 in II Peg, and 15 in V711 Tau. Lifetimes of individual spots ranged from a few months to longer than 6 yr. Differential rotation coefficients, estimated from the observed range of spot rotation periods for each star and defined by equation (2), were 0.04 for lambda And, 0.038 for sigma Gem, 0.005 for II Peg, and 0.006 for V711 Tau, versus 0.19 for the Sun. We searched for cyclic changes in mean brightness, B-V color index, and spot rotation period as evidence for long-term cycles. Of these, long-term variability in mean brightness appears to offer the best evidence for such cycles in these four stars. Cycles of 11.1 yr for lambda And, 8.5 yr for sigma Gem, 11 yr for II Peg, and 16 yr V711 Tau are implied by these mean brightness changes. Cyclic changes in spot rotation period were found in lambda And and possibly II Peg. Errors in B-V were too large for any long-term changes to be detectable.